Help me with average rate of change calculations it's f(x+h)-f(x)/h and f(x)=x^4 with point (-1,1). How does it equal -4? I can't get it, I only get 4

Question

campbell_st · Answer

ok... well this is differentiation b 1st principles... 

which will be long and tedious

$$f(x + h) = (x + h)^4 = x^4 + 4x^3h + 6x^2h^2 + 4xh^3 + h^4 $$

and 

$$f(x) = x^4$$

substitute them and you should also have a limit

$$\lim_{h \rightarrow 0}\frac{x^4 + 4x^3h + 6x^2h^2 + 4xh^3 + h^4 - x^4}{h}$$

collect like terms in the numerator

then factor the numerator 

look for common factors between the numerator and denominator

substitute the limit

and you will have 

f'(x) 

then find 

f'(-1), that is substitute x = -1 from the point and evaluate

anonymous · Answer

yeah I was dumb I didn't foil properly thanks lol